Modelo de fijación de precios de activos de capital (CAPM)
El modelo de fijación de precios de activos de capital (CAPM, por sus siglas en inglés) indica cuál debería ser la tasa de rendimiento esperada o requerida sobre activos de riesgo como las acciones ordinarias de Dollar Tree.
Tasas de retorno
Dollar Tree Inc., tasas mensuales de retorno
| Dollar Tree Inc. (DLTR) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioDLTR,t1 | DividendoDLTR,t1 | RDLTR,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 29 feb. 2016 | $80.25 | 1,932.23 | ||||
| 1. | 31 mar. 2016 | $82.46 | 2.75% | 2,059.74 | 6.60% | |
| 2. | 30 abr. 2016 | $79.71 | -3.33% | 2,065.30 | 0.27% | |
| 3. | 31 may. 2016 | $90.54 | 13.59% | 2,096.95 | 1.53% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 31 dic. 2021 | $140.52 | 5.00% | 4,766.18 | 4.36% | |
| 71. | 31 ene. 2022 | $131.22 | -6.62% | 4,515.55 | -5.26% | |
| Promedio (R): | 1.08% | 1.29% | ||||
| Desviación estándar: | 8.96% | 4.25% | ||||
| Dollar Tree Inc. (DLTR) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioDLTR,t1 | DividendoDLTR,t1 | RDLTR,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 29 feb. 2016 | $80.25 | 1,932.23 | ||||
| 1. | 31 mar. 2016 | $82.46 | 2.75% | 2,059.74 | 6.60% | |
| 2. | 30 abr. 2016 | $79.71 | -3.33% | 2,065.30 | 0.27% | |
| 3. | 31 may. 2016 | $90.54 | 13.59% | 2,096.95 | 1.53% | |
| 4. | 30 jun. 2016 | $94.24 | 4.09% | 2,098.86 | 0.09% | |
| 5. | 31 jul. 2016 | $96.29 | 2.18% | 2,173.60 | 3.56% | |
| 6. | 31 ago. 2016 | $82.70 | -14.11% | 2,170.95 | -0.12% | |
| 7. | 30 sept. 2016 | $78.93 | -4.56% | 2,168.27 | -0.12% | |
| 8. | 31 oct. 2016 | $75.55 | -4.28% | 2,126.15 | -1.94% | |
| 9. | 30 nov. 2016 | $88.16 | 16.69% | 2,198.81 | 3.42% | |
| 10. | 31 dic. 2016 | $77.18 | -12.45% | 2,238.83 | 1.82% | |
| 11. | 31 ene. 2017 | $77.19 | 0.01% | 2,278.87 | 1.79% | |
| 12. | 28 feb. 2017 | $76.68 | -0.66% | 2,363.64 | 3.72% | |
| 13. | 31 mar. 2017 | $78.46 | 2.32% | 2,362.72 | -0.04% | |
| 14. | 30 abr. 2017 | $82.77 | 5.49% | 2,384.20 | 0.91% | |
| 15. | 31 may. 2017 | $77.70 | -6.13% | 2,411.80 | 1.16% | |
| 16. | 30 jun. 2017 | $69.92 | -10.01% | 2,423.41 | 0.48% | |
| 17. | 31 jul. 2017 | $72.08 | 3.09% | 2,470.30 | 1.93% | |
| 18. | 31 ago. 2017 | $79.64 | 10.49% | 2,471.65 | 0.05% | |
| 19. | 30 sept. 2017 | $86.82 | 9.02% | 2,519.36 | 1.93% | |
| 20. | 31 oct. 2017 | $91.25 | 5.10% | 2,575.26 | 2.22% | |
| 21. | 30 nov. 2017 | $102.76 | 12.61% | 2,647.58 | 2.81% | |
| 22. | 31 dic. 2017 | $107.31 | 4.43% | 2,673.61 | 0.98% | |
| 23. | 31 ene. 2018 | $115.00 | 7.17% | 2,823.81 | 5.62% | |
| 24. | 28 feb. 2018 | $102.64 | -10.75% | 2,713.83 | -3.89% | |
| 25. | 31 mar. 2018 | $94.90 | -7.54% | 2,640.87 | -2.69% | |
| 26. | 30 abr. 2018 | $95.89 | 1.04% | 2,648.05 | 0.27% | |
| 27. | 31 may. 2018 | $82.59 | -13.87% | 2,705.27 | 2.16% | |
| 28. | 30 jun. 2018 | $85.00 | 2.92% | 2,718.37 | 0.48% | |
| 29. | 31 jul. 2018 | $91.28 | 7.39% | 2,816.29 | 3.60% | |
| 30. | 31 ago. 2018 | $80.51 | -11.80% | 2,901.52 | 3.03% | |
| 31. | 30 sept. 2018 | $81.55 | 1.29% | 2,913.98 | 0.43% | |
| 32. | 31 oct. 2018 | $84.30 | 3.37% | 2,711.74 | -6.94% | |
| 33. | 30 nov. 2018 | $86.77 | 2.93% | 2,760.17 | 1.79% | |
| 34. | 31 dic. 2018 | $90.32 | 4.09% | 2,506.85 | -9.18% | |
| 35. | 31 ene. 2019 | $96.83 | 7.21% | 2,704.10 | 7.87% | |
| 36. | 28 feb. 2019 | $96.33 | -0.52% | 2,784.49 | 2.97% | |
| 37. | 31 mar. 2019 | $105.04 | 9.04% | 2,834.40 | 1.79% | |
| 38. | 30 abr. 2019 | $111.28 | 5.94% | 2,945.83 | 3.93% | |
| 39. | 31 may. 2019 | $101.59 | -8.71% | 2,752.06 | -6.58% | |
| 40. | 30 jun. 2019 | $107.39 | 5.71% | 2,941.76 | 6.89% | |
| 41. | 31 jul. 2019 | $101.75 | -5.25% | 2,980.38 | 1.31% | |
| 42. | 31 ago. 2019 | $101.53 | -0.22% | 2,926.46 | -1.81% | |
| 43. | 30 sept. 2019 | $114.16 | 12.44% | 2,976.74 | 1.72% | |
| 44. | 31 oct. 2019 | $110.40 | -3.29% | 3,037.56 | 2.04% | |
| 45. | 30 nov. 2019 | $91.46 | -17.16% | 3,140.98 | 3.40% | |
| 46. | 31 dic. 2019 | $94.05 | 2.83% | 3,230.78 | 2.86% | |
| 47. | 31 ene. 2020 | $87.07 | -7.42% | 3,225.52 | -0.16% | |
| 48. | 29 feb. 2020 | $83.03 | -4.64% | 2,954.22 | -8.41% | |
| 49. | 31 mar. 2020 | $73.47 | -11.51% | 2,584.59 | -12.51% | |
| 50. | 30 abr. 2020 | $79.67 | 8.44% | 2,912.43 | 12.68% | |
| 51. | 31 may. 2020 | $97.87 | 22.84% | 3,044.31 | 4.53% | |
| 52. | 30 jun. 2020 | $92.68 | -5.30% | 3,100.29 | 1.84% | |
| 53. | 31 jul. 2020 | $93.35 | 0.72% | 3,271.12 | 5.51% | |
| 54. | 31 ago. 2020 | $96.27 | 3.13% | 3,500.31 | 7.01% | |
| 55. | 30 sept. 2020 | $91.34 | -5.12% | 3,363.00 | -3.92% | |
| 56. | 31 oct. 2020 | $90.32 | -1.12% | 3,269.96 | -2.77% | |
| 57. | 30 nov. 2020 | $109.24 | 20.95% | 3,621.63 | 10.75% | |
| 58. | 31 dic. 2020 | $108.04 | -1.10% | 3,756.07 | 3.71% | |
| 59. | 31 ene. 2021 | $101.66 | -5.91% | 3,714.24 | -1.11% | |
| 60. | 28 feb. 2021 | $98.20 | -3.40% | 3,811.15 | 2.61% | |
| 61. | 31 mar. 2021 | $114.46 | 16.56% | 3,972.89 | 4.24% | |
| 62. | 30 abr. 2021 | $114.90 | 0.38% | 4,181.17 | 5.24% | |
| 63. | 31 may. 2021 | $97.50 | -15.14% | 4,204.11 | 0.55% | |
| 64. | 30 jun. 2021 | $99.50 | 2.05% | 4,297.50 | 2.22% | |
| 65. | 31 jul. 2021 | $99.79 | 0.29% | 4,395.26 | 2.27% | |
| 66. | 31 ago. 2021 | $90.54 | -9.27% | 4,522.68 | 2.90% | |
| 67. | 30 sept. 2021 | $95.72 | 5.72% | 4,307.54 | -4.76% | |
| 68. | 31 oct. 2021 | $107.76 | 12.58% | 4,605.38 | 6.91% | |
| 69. | 30 nov. 2021 | $133.83 | 24.19% | 4,567.00 | -0.83% | |
| 70. | 31 dic. 2021 | $140.52 | 5.00% | 4,766.18 | 4.36% | |
| 71. | 31 ene. 2022 | $131.22 | -6.62% | 4,515.55 | -5.26% | |
| Promedio (R): | 1.08% | 1.29% | ||||
| Desviación estándar: | 8.96% | 4.25% | ||||
Mostrar todo
1 Datos en dólares estadounidenses por acción ordinaria, ajustados por divisiones y dividendos de acciones.
2 Tasa de rendimiento de las existencias ordinarias de DLTR durante el período t.
3 Tasa de rendimiento del S&P 500 (el proxy de la cartera de mercado) durante el período t.
Varianza y covarianza
Dollar Tree Inc., cálculo de la varianza y covarianza de los rendimientos
| t | Fecha | RDLTR,t | RS&P 500,t | (RDLTR,t–RDLTR)2 | (RS&P 500,t–RS&P 500)2 | (RDLTR,t–RDLTR)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 31 mar. 2016 | 2.75% | 6.60% | 2.79 | 28.16 | 8.87 |
| 2. | 30 abr. 2016 | -3.33% | 0.27% | 19.52 | 1.05 | 4.52 |
| 3. | 31 may. 2016 | 13.59% | 1.53% | 156.34 | 0.06 | 3.00 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 31 dic. 2021 | 5.00% | 4.36% | 15.33 | 9.42 | 12.02 |
| 71. | 31 ene. 2022 | -6.62% | -5.26% | 59.31 | 42.91 | 50.45 |
| Total (Σ): | 5,617.47 | 1,262.70 | 1,008.02 | |||
| t | Fecha | RDLTR,t | RS&P 500,t | (RDLTR,t–RDLTR)2 | (RS&P 500,t–RS&P 500)2 | (RDLTR,t–RDLTR)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 31 mar. 2016 | 2.75% | 6.60% | 2.79 | 28.16 | 8.87 |
| 2. | 30 abr. 2016 | -3.33% | 0.27% | 19.52 | 1.05 | 4.52 |
| 3. | 31 may. 2016 | 13.59% | 1.53% | 156.34 | 0.06 | 3.00 |
| 4. | 30 jun. 2016 | 4.09% | 0.09% | 9.02 | 1.44 | -3.61 |
| 5. | 31 jul. 2016 | 2.18% | 3.56% | 1.19 | 5.15 | 2.48 |
| 6. | 31 ago. 2016 | -14.11% | -0.12% | 230.94 | 2.00 | 21.49 |
| 7. | 30 sept. 2016 | -4.56% | -0.12% | 31.83 | 2.00 | 7.99 |
| 8. | 31 oct. 2016 | -4.28% | -1.94% | 28.79 | 10.46 | 17.36 |
| 9. | 30 nov. 2016 | 16.69% | 3.42% | 243.61 | 4.52 | 33.17 |
| 10. | 31 dic. 2016 | -12.45% | 1.82% | 183.27 | 0.28 | -7.15 |
| 11. | 31 ene. 2017 | 0.01% | 1.79% | 1.14 | 0.25 | -0.53 |
| 12. | 28 feb. 2017 | -0.66% | 3.72% | 3.04 | 5.89 | -4.23 |
| 13. | 31 mar. 2017 | 2.32% | -0.04% | 1.53 | 1.77 | -1.65 |
| 14. | 30 abr. 2017 | 5.49% | 0.91% | 19.45 | 0.15 | -1.69 |
| 15. | 31 may. 2017 | -6.13% | 1.16% | 51.96 | 0.02 | 0.97 |
| 16. | 30 jun. 2017 | -10.01% | 0.48% | 123.12 | 0.66 | 9.00 |
| 17. | 31 jul. 2017 | 3.09% | 1.93% | 4.03 | 0.41 | 1.29 |
| 18. | 31 ago. 2017 | 10.49% | 0.05% | 88.46 | 1.53 | -11.64 |
| 19. | 30 sept. 2017 | 9.02% | 1.93% | 62.93 | 0.41 | 5.06 |
| 20. | 31 oct. 2017 | 5.10% | 2.22% | 16.16 | 0.86 | 3.72 |
| 21. | 30 nov. 2017 | 12.61% | 2.81% | 132.96 | 2.30 | 17.48 |
| 22. | 31 dic. 2017 | 4.43% | 0.98% | 11.19 | 0.10 | -1.03 |
| 23. | 31 ene. 2018 | 7.17% | 5.62% | 37.01 | 18.71 | 26.31 |
| 24. | 28 feb. 2018 | -10.75% | -3.89% | 139.97 | 26.90 | 61.37 |
| 25. | 31 mar. 2018 | -7.54% | -2.69% | 74.37 | 15.85 | 34.33 |
| 26. | 30 abr. 2018 | 1.04% | 0.27% | 0.00 | 1.04 | 0.04 |
| 27. | 31 may. 2018 | -13.87% | 2.16% | 223.59 | 0.75 | -12.99 |
| 28. | 30 jun. 2018 | 2.92% | 0.48% | 3.37 | 0.65 | -1.48 |
| 29. | 31 jul. 2018 | 7.39% | 3.60% | 39.76 | 5.34 | 14.56 |
| 30. | 31 ago. 2018 | -11.80% | 3.03% | 165.94 | 3.01 | -22.34 |
| 31. | 30 sept. 2018 | 1.29% | 0.43% | 0.04 | 0.74 | -0.18 |
| 32. | 31 oct. 2018 | 3.37% | -6.94% | 5.24 | 67.78 | -18.85 |
| 33. | 30 nov. 2018 | 2.93% | 1.79% | 3.41 | 0.24 | 0.91 |
| 34. | 31 dic. 2018 | 4.09% | -9.18% | 9.05 | 109.62 | -31.50 |
| 35. | 31 ene. 2019 | 7.21% | 7.87% | 37.51 | 43.25 | 40.28 |
| 36. | 28 feb. 2019 | -0.52% | 2.97% | 2.56 | 2.82 | -2.69 |
| 37. | 31 mar. 2019 | 9.04% | 1.79% | 63.34 | 0.25 | 3.98 |
| 38. | 30 abr. 2019 | 5.94% | 3.93% | 23.60 | 6.96 | 12.82 |
| 39. | 31 may. 2019 | -8.71% | -6.58% | 95.86 | 61.94 | 77.05 |
| 40. | 30 jun. 2019 | 5.71% | 6.89% | 21.40 | 31.37 | 25.91 |
| 41. | 31 jul. 2019 | -5.25% | 1.31% | 40.13 | 0.00 | -0.13 |
| 42. | 31 ago. 2019 | -0.22% | -1.81% | 1.69 | 9.62 | 4.03 |
| 43. | 30 sept. 2019 | 12.44% | 1.72% | 128.97 | 0.18 | 4.84 |
| 44. | 31 oct. 2019 | -3.29% | 2.04% | 19.15 | 0.56 | -3.29 |
| 45. | 30 nov. 2019 | -17.16% | 3.40% | 332.65 | 4.46 | -38.53 |
| 46. | 31 dic. 2019 | 2.83% | 2.86% | 3.06 | 2.45 | 2.74 |
| 47. | 31 ene. 2020 | -7.42% | -0.16% | 72.33 | 2.12 | 12.37 |
| 48. | 29 feb. 2020 | -4.64% | -8.41% | 32.75 | 94.15 | 55.53 |
| 49. | 31 mar. 2020 | -11.51% | -12.51% | 158.68 | 190.56 | 173.89 |
| 50. | 30 abr. 2020 | 8.44% | 12.68% | 54.11 | 129.78 | 83.80 |
| 51. | 31 may. 2020 | 22.84% | 4.53% | 473.55 | 10.47 | 70.42 |
| 52. | 30 jun. 2020 | -5.30% | 1.84% | 40.78 | 0.30 | -3.49 |
| 53. | 31 jul. 2020 | 0.72% | 5.51% | 0.13 | 17.79 | -1.52 |
| 54. | 31 ago. 2020 | 3.13% | 7.01% | 4.18 | 32.65 | 11.69 |
| 55. | 30 sept. 2020 | -5.12% | -3.92% | 38.49 | 27.20 | 32.35 |
| 56. | 31 oct. 2020 | -1.12% | -2.77% | 4.84 | 16.47 | 8.93 |
| 57. | 30 nov. 2020 | 20.95% | 10.75% | 394.61 | 89.54 | 187.97 |
| 58. | 31 dic. 2020 | -1.10% | 3.71% | 4.76 | 5.86 | -5.28 |
| 59. | 31 ene. 2021 | -5.91% | -1.11% | 48.83 | 5.79 | 16.81 |
| 60. | 28 feb. 2021 | -3.40% | 2.61% | 20.13 | 1.73 | -5.91 |
| 61. | 31 mar. 2021 | 16.56% | 4.24% | 239.48 | 8.71 | 45.68 |
| 62. | 30 abr. 2021 | 0.38% | 5.24% | 0.49 | 15.60 | -2.76 |
| 63. | 31 may. 2021 | -15.14% | 0.55% | 263.30 | 0.55 | 12.07 |
| 64. | 30 jun. 2021 | 2.05% | 2.22% | 0.94 | 0.86 | 0.90 |
| 65. | 31 jul. 2021 | 0.29% | 2.27% | 0.63 | 0.97 | -0.78 |
| 66. | 31 ago. 2021 | -9.27% | 2.90% | 107.17 | 2.58 | -16.63 |
| 67. | 30 sept. 2021 | 5.72% | -4.76% | 21.51 | 36.59 | -28.06 |
| 68. | 31 oct. 2021 | 12.58% | 6.91% | 132.14 | 31.61 | 64.63 |
| 69. | 30 nov. 2021 | 24.19% | -0.83% | 534.06 | 4.52 | -49.12 |
| 70. | 31 dic. 2021 | 5.00% | 4.36% | 15.33 | 9.42 | 12.02 |
| 71. | 31 ene. 2022 | -6.62% | -5.26% | 59.31 | 42.91 | 50.45 |
| Total (Σ): | 5,617.47 | 1,262.70 | 1,008.02 | |||
Mostrar todo
VarianzaDLTR = Σ(RDLTR,t–RDLTR)2 ÷ (71 – 1)
= 5,617.47 ÷ (71 – 1)
= 80.25
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,262.70 ÷ (71 – 1)
= 18.04
CovarianzaDLTR, S&P 500 = Σ(RDLTR,t–RDLTR)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 1,008.02 ÷ (71 – 1)
= 14.40
Estimación sistemática del riesgo (β)
| VarianzaDLTR | 80.25 |
| VarianzaS&P 500 | 18.04 |
| CovarianzaDLTR, S&P 500 | 14.40 |
| Coeficiente de correlaciónDLTR, S&P 5001 | 0.38 |
| βDLTR2 | 0.80 |
| αDLTR3 | 0.05% |
Cálculos
1 Coeficiente de correlaciónDLTR, S&P 500
= CovarianzaDLTR, S&P 500 ÷ (Desviación estándarDLTR × Desviación estándarS&P 500)
= 14.40 ÷ (8.96% × 4.25%)
= 0.38
2 βDLTR
= CovarianzaDLTR, S&P 500 ÷ VarianzaS&P 500
= 14.40 ÷ 18.04
= 0.80
3 αDLTR
= PromedioDLTR – βDLTR × PromedioS&P 500
= 1.08% – 0.80 × 1.29%
= 0.05%
Tasa de rendimiento esperada
| Suposiciones | ||
| Tasa de rendimiento del LT Treasury Composite1 | RF | 4.68% |
| Tasa de rendimiento esperada de la cartera de mercado2 | E(RM) | 13.78% |
| Riesgo sistemático de Dollar Tree acciones ordinarias | βDLTR | 0.80 |
| Tasa de rendimiento esperada de las acciones ordinarias de Dollar Tree3 | E(RDLTR) | 11.95% |
1 Promedio no ponderado de los rendimientos de las ofertas de todos los bonos del Tesoro de EE. UU. con cupón fijo en circulación que no vencen ni son rescatables en menos de 10 años (proxy de tasa de rendimiento libre de riesgo).
3 E(RDLTR) = RF + βDLTR [E(RM) – RF]
= 4.68% + 0.80 [13.78% – 4.68%]
= 11.95%